Directional rock blasting using shaped charges using combined charge liners with different shapes

The shape of a charge liner used in shaped charges with a combined liner will greatly influence the blasting effect. In this study, we examined how combined charge liners with different shapes affected directional rock blasting, and we assessed the influence mechanism. The numerical simulation results showed that among the three shaped charge liners, liners with arc and triangular shapes performed significantly better than the flat‐top liner, and the triangular liner was slightly superior to the arc‐shaped liner. Model testing indicated that principal cracks in the arc‐shaped and triangular liners developed along the combined energy‐gathering direction, while the principal cracks of the flat‐top liner deviated 32° from the axis. Therefore, the directional cracking effect of arc‐shaped and triangular liners was superior to the flat‐top liner. According to the peak strain values on the liners, the peak strain in the combined energy‐gathering direction was greater than that in the slot and nonenergy‐gathering directions, and the order of the peak strain of the three liners followed arc‐shaped liner > triangular liner > flat‐top liner. The directional blasting effect of the triangular liner was slightly better than the arc‐shaped liner. In conclusion, the findings of this study suggested that the best directional rock‐blasting effect was achieved when the shape of the combined charge liner was triangular.

1][12][13][14][15] In the 1970s, Fourney et al. conducted a series of experiments using a charge with a slotted tube, and the results demonstrated that this method achieved effective fracture control in blasting. 16,17For example, Zhu et al. 14 investigated the effect of coupling medium and decoupling coefficients on blast-induced rock fracture by using AUTODYN, and found that the coupling material has a significant effect on the degree of damage to the rock.By simulating rock fracture under blasting loads with LS-DYNA, Ma and An, 13 it was shown that the loading rate, pre-existing nodal surfaces, and ground stress affect rock fragmentation.Kabwe 18 compared traditional blasting techniques with the top air-deck blasting technique, and found that the latter significantly reduced explosive load and effectively fragmented the muckpile material.Wang 19 analyzed the influence of the filling medium between the blast hole and the explosive on the blasting effect of a slotted charge using numerical simulations and dynamic caustics tests.Yue and coworkers [20][21][22][23] utilized a digital laser dynamic caustics system to study crack propagation using the slotted cartridge blasting technique, obtaining the speed and acceleration of crack propagation, the dynamic stress intensity factor at the front of the crack, and the dynamic energy release rate.Furthermore, Yue et al. 24 studied the relationship between the blasting waves and a running crack produced by slotted charge blasting.
Shaped charges have been widely used in tandem combatants and torpedoes to strike various targets, 25,26 as they can directionally concentrate the denotation energy, inducing stress concentration and facilitating directional crack propagation. 27Huang 28 proposed the uniform jet flow theory according to the mechanism of shaped charges, in which the jet velocity and length were simplified as constants.Specifically, it was assumed that the target was in a pure fluid state when the jet flow penetrated the target, while the strength of the target and metal jet flow were ignored.Allison and Vitali 29 detected the velocity gradient in the velocity direction of a shaped jet during experiments and proposed the nonuniform jet flow theory.Zhang et al. 30 analyzed the influence of explosively formed pellet shapes on the velocity and stress distribution of the jet.Wang et al. 31 conducted penetration tests of shaped charges into concrete specimens, and found a quadratic correlation between the penetration depth, crater diameter, and jet velocity.Yin et al. 32 demonstrated that decoupling bilateral-grooveslot-shaped charge blasting resulted in the best blasting effect, as indicated by long directional cracks, few nondirectional cracks, and minimal damage to the surrounding rock.Bhagat et al. 33 proposed a directionally controlled blasting technique for railroad tracks, which allows blasting works to be carried out without affecting the train counterparts (2-3 m from the slope).Both slotted and shaped charges have shown good energy concentration and directional rock-breaking effects, 34 suggesting the potential for integrating these two structures into a new combined charge.
On the basis of combined charges, in this study, we investigated the crack distribution and stress-strain evolution characteristics under the influence of three liner shapes using theoretical analysis, numerical simulations, and model testing.The optimal liner shape was determined to optimize the directional blasting effect of the combined charge, thus, resolving the above-described problems and providing a reference for the development of directional blasting theories.

| PRINCIPLE OF COMBINED CHARGE BLASTING
Combined charges consist of a charging structure that combines a shaped charge and a slotted charge.In this structure, a slotted tube is placed on the outer layer of the shaped charge, giving the combined charge a dual energy-gathering effect due to the metal jet of the shaped charge and the detonation gas of the slotted charge.In traditional blasting, no energy gathering will occur, and hence, the cracks will propagate irregularly.By contrast, combined charges utilize the cavitation effect, converting explosive energy into kinetic energy after detonation, so that the metal liner forms a jet. 35The jet penetrates the initial guiding slot at the edge of the blast hole, providing directional support for crack propagation under the blasting wave and detonation gas.The slotted tube in the combined charge controls the stress field distribution, as well as the quasistatic and wedge effects of the detonation gas on the medium.These factors work together to achieve directional blasting.A dynamic rock fracture model under combined charge blasting was established, according to rock fracture mechanics, as shown in Figure 1.
During crack propagation, the stress intensity factor at the crack tip can be expressed by where P is the pressure of the detonation gas in the crack, F is a correction term of the stress intensity factor, r b denotes the radius of the blast hole, a is the length of the crack, and σ θ denotes the tangential stress.
According to fracture mechanics, cracks will initiate when K 1 > K IC , where K IC represents the fracture toughness of the rock.Therefore, to ensure continuous crack propagation, the pressure of the detonation gas will need to satisfy the following condition: The shaped charge jet has a strong penetration ability, with guiding cracks in the energy-gathering direction significantly larger than the cracks in the fragmentation zone.The blasting energy flow itself will exhibit a high density and small area, with the slotted tube capable of restraining the detonation products, thus, concentrating the energy flow in the direction of the slot.A large amount of high-pressure detonation gas will enter the guiding cracks, with the pressure of the detonation gas in the energy-gathering direction increasing accordingly, namely, an increase in the value of P.Under the quasistatic condition, the initial cracks caused by the stress wave will further expand. 13,36According to the law of conservation of energy, the pressure of the detonation gas in the nonenergy-gathering direction will weaken.Therefore, combined charges improve the blasting ability in the energy-gathering direction, while protecting the surrounding rock in the nonenergygathering direction.
Through the analysis of the principle of combined polymerization rock breaking, the intrinsic connection between the combined polymerization packages, polymerization packages, and slit packages was obtained, and the fracturing analysis of the rock body was carried out based on the mechanism of rock breaking of the polymerization packages and slit packages, and the conditions for the directional fracturing of the rock body were obtained.

| NUMERICAL SIMULATIONS
Combined polycondensation packet drilling and blasting process is complex and rapid, it is not easy to directly observe, so the use of LS-DYNA software to simulate the spiral tube polycondensation packet penetration process.Through the simulation can be visualized to show how the metal jet is formed and moved, but also to get the pressure map and post-blast damage crack distribution map and other data, and to analyze the directional energy effect of different polymerization covers.

| Simulation model
To compare the effects of the combined charge and the slotted charge, a numerical model composed of explosives, polyvinyl chloride (PVC) tubes, aluminum tubes, copper charge liners, concrete target plates, and air was constructed.The model utilized the cm-g-μs unit system.The explosives, air, and copper were meshed using Eulerian meshes, employing the multimaterial arbitrary Lagrangian-Eulerian (ALE) algorithm.Lagrangian meshes were used for the PVC tubes, aluminum tubes, and concrete target plates.The contacts in the model were simulated using the fluid-solid coupling algorithm, and the boundary conditions are set to nonreflective boundary conditions.To reduce computational load, a two-dimensional (2D) single-layer solid mesh model was established (Figure 2), and the charge model is shown in Figure 3.The 2D model reduced the model size, which saved calculation time, and made full use of the multimaterial ALE algorithm in LS-DYNA.
The *MAT_HIGH_EXPLOSIVE_BURN constitutive model was used in the model for the main charge, and the Jones-Wilkins-Lee state equation was used to represent the relationship between the pressure, volume, and energy of the detonation products, the relevant material parameters of the explosive 9 are shown in Table 1.The Johnson-Cook constitutive model and the Gruneisen state equation were used for the copper charge liner, the relevant material parameters of the copper charge liner are shown in Table 2.The MAT_PLASTIC_KINE_ MATIC constitutive model was used for the PVC tube, the relevant material parameters of the PVC tube 37 are shown in Table 3.In addition, the Johnson-Cook constitutive model and Gruneisen state equation were used for the aluminum slotted tube, the relevant material parameters of the aluminum slotted tube are shown in Table 4. Air was described by the *MAT_NULL constitutive model and the LINEAR_POLYNOMIAL state equation, the relevant material parameters of the air 38 are shown in Table 5.The JOHNSON_HOLMQUIST_CONCRETE constitutive model can well describe the mechanical behavior of the material under strong dynamic loads, and the number of parameters of the model is relatively small and the physical meaning is clear, so the concrete target plate was described by the JOHNSON_HOLMQUIST_CONCRETE constitutive model, the relevant material parameters of the concrete target plate 38 are shown in Table 6.

| Results
(1) Shape analysis of the metal jet We assessed the jet formation process of three types of charge liners in the combined charge, namely, the arcshaped, triangular, and flat-top liners.We found that the morphological characteristics of the jets were the most obvious at T = 5.41 μs, as shown in Figure 4.
Circular arc-shaped fusion hood in the direction of the fusion of explosives and circular arc-shaped fusion hood in contact with the effective area is relatively large, so that the metal fusion hood in the explosion occurred after the explosion to get more energy, which makes the metal jet speed faster.However, the arc-shaped cover due to the relatively uniform force, so the metal jet velocity gradient is small, resulting in a short period of time the metal jet cannot get enough stretching, so that the metal jet shape is relatively short and thick, in the penetration of the exploded rock body when the opening is larger.Triangular polycondensation cover characteristics and arc-shaped polycondensation cover is just the opposite, in the direction of polycondensation, explosives and triangular polycondensation cover of the effective contact area is relatively small, the explosion energy is easy to converge in the triangle polycondensation cover at the top of the formation of a smaller tail speed and a larger head speed of the metal jet, and a larger velocity gradient effectively enhance the length of the metal jet axis of the direction of the tensile force, so that within a short period of time, the metal jet is stretched relatively slender, which in turn improves the aggregation of metal jets, the rock body being blasted after the action produced slender cracks.However, the metal jet velocity gradient increases at the same time, will lead to the metal jet to reach the stretching limit of the time is reduced, resulting in the metal jet is easy to be pulled off, so that the energy diffusion, resulting in a reduction in the depth of penetration.The effective area of the middle part of the flat-top-shaped energy concentrator in contact with the explosives is relatively large, and the contact area of the two ends is relatively small, which makes the metal jet in the middle of the energy concentrator faster, and the speed of the metal jet at the two ends is obviously  slower than that in the middle of the metal jet, and finally the metal jet is disconnected under the effect of the difference in speed, which makes the effect of energy concentrating poorer in the infiltration of the rock body.
It is concluded that the directional rock-breaking ability of arc-shaped and triangular-shaped fusion hoods is better than that of flat-top-shaped fusion hoods, while the metal jets of triangular-shaped fusion hoods are slender, and the fissure openings are small and long when fracturing, so the directional rock-breaking ability is better than that of arc-shaped fusion hoods.Therefore, the triangular-shaped fusion hood is more advantageous than the arc-shaped and flat-top-shaped fusion hoods for directional control of rock breaking.
(2) Pressure map of different liners The effects of three jets penetrating rock targets were compared with analyze the penetration performance of the three liners.The pressure map at T = 6.1 μs is shown in Figure 5.
After the jet formed following detonation, the peak pressure in the axial direction of the combined charge was higher than in the slot direction, and the arc-shaped liner demonstrated the most severe pressure concentration, followed by the triangular and flat-top liners.The peak pressure of the flat-top liner was small, indicating a poor energy-gathering effect.Moreover, obvious deformation of the slotted tube was observed in the axial direction of the combined charge with arc-shaped and triangular liners, and the deformation was relatively small in the other directions.For the flat-top liner, the entire slotted tube showed a large deformation.Therefore, we concluded that the arc-shaped and triangular liners demonstrated better directional energy-gathering performance compared with the flat-top liner.
(3) Crack analysis Figure 6 shows the cracks that formed after detonation, indicating that a void formed around the blast hole when the concrete around the blast hole was fragmented by the high-pressure explosion, resulting in the fragmentation zone.Principal cracks gradually expanded along the radial direction of the blast hole from the fragmentation zone, and continued to develop along the initial direction.In all three liners, principal cracks in the energy-gathering direction exhibited a significantly larger width and length compared with the principal cracks in the slot direction.As a result, the energy-gathering effect in the energy-gathering direction was superior to the slot direction.Additionally, secondary cracks were produced in the triangular liner that penetrated from the fragmentation zone to the edge of the model, surpassing the penetration distances achieved by the arc-shaped and flat-top liners.In terms of the secondary crack distribution, the secondary cracks in the triangular liner had the smallest opening angle, which was almost parallel to the principal cracks, suggesting a good directional blasting effect.This was followed by the flat-top liner, while the arc-shaped liner displayed the worst distribution.In summary, the triangular liner exhibited the best directional rock-blasting effect.

| PRECRACKING BLASTING TESTS
To verify the directional penetration of the hole wall and the polymerization effect of the combination of energy packs, the design of the drilling and blasting test, which mainly consists of C30 strength  study are shown in Figure 7.The explosives consisted of No. 2 rock emulsion explosives from the same batch, and the density of the line charge was 1-1.25 g/cm 3 .For the test, liners with three different shapes (arc, triangle, and flat-top) were selected, along with three concrete samples.The test was carried out in a testing facility, and the test parameters are shown in Table 7.
(1) Charge structure The combined charge used in the test was composed of a charge liner, a main charge, and a detonator.The shaped charge liner was composed of copper, with a thickness of 0.1 mm.The energy-gathering tubes were composed of PVC, with a wall thickness of 1 mm and an inner diameter of 18 mm.The slotted tube was made of aluminum, with a thickness of 2 mm.After optimization, the decoupling coefficient was set to 1.78.The variable was the shape of the liner.The combined charge is shown in Figure 8.
(2) Strain gauges Three dynamic strain gauges were attached to the top of each concrete sample in each combined energy-gathering direction, namely, the single energy-gathering direction and the nonenergy-gathering direction.The spacing between the strain gauges was 5.5 cm.In addition, one additional strain gauge was attached to the center of the concrete wall in three directions, starting 5 cm from the blast hole with a spacing of 5 cm.Three velocity sensors were attached to the top surface of the sample in the single energy-gathering and dual energy-gathering directions.The layout of the strain gauges and sensors is shown in Figure 9.

| Crack distribution characteristics
Three groups of tests were carried out to investigate the influence of the liner shape on the directional blasting effect of the combined charge and analyze the crack distribution characteristics.The data are shown in Table 8, and the crack distribution is shown in Figure 10.
As shown in Table 2 and Figure 10, in the combined energy-gathering direction, all three liners contained an axial crack from the center of the blast hole to the edge | 4387 of the concrete sample, and the principal crack of the arc-shaped and triangular liners did not shift.However, the principal crack of the flat-top liner had a 32°offset.
In the slot direction, the arc-shaped and triangular liners produced a complete crack from the center of the blast hole to the edge of the sample, and the principal crack propagated in the axial direction.By contrast, the flat-top liner produced two cracks without obvious directionality.For the arc-shaped and triangular liners, the penetration distance in the energy-gathering direction was greater than in the single-energy-gathering direction, while for the flat-top liner, the penetration distance in the energy-gathering direction was smaller than the single slot direction.In addition, we found that the width of the cracks in the combined energygathering direction was greater than in the single slot direction.The triangular liner cracks were slender, indicating an excellent directional blasting effect.This was followed by the arc-shaped liner, while the flat-top line exhibited the worst effect.Regarding the cracks in the nonenergy-gathering direction, the arc-shaped liner produced only two hairline cracks in the sample, and the triangular liner produced four normal cracks, while the flat-top liner had two wide cracks.Therefore, the arc-shaped liner provided the best protection for the surrounding rock, followed by the triangular and flat-top liners.
Considering the above results for the cracks in the three samples, and by comprehensively evaluating the crack width, the offset angle along the cracking direction, and the penetration distance along the cracking direction, we concluded that the triangular liner had the best directional precracking effect.

| Strain analysis
In this study, ultradynamic strain gauges were used for data acquisition of the concrete samples.Figure 11 presents the strain waveform of the three concrete samples penetrated by the arc-shaped, triangular, and flat-top liners.
The following observations were made by analyzing the time history of the above strain waveform.
F I G U R E 9 Layout of the strain gauges.
T A B L E 8 Data summary after explosion.(1) The overall variation trend of the strain waveform was similar among the three samples.For the slotted tube on the liner side, the peak strain generally occurred earlier than in the single energy-gathering and nonenergy-gathering directions, and the magnitude of the peak strain was larger than in the two directions.Moreover, we observed that the strain value in the combined energy-gathering direction at measuring point #2 was larger than at measuring points #1 and #3.(2) According to the above waveforms, the process generally consisted of three stages.The first was the compressive strain stage, which lasted approximately 50 μs from the start time.During this stage, the strain suddenly increased to the peak value and then transitioned into tensile strain.The second stage was the tensile strain stage, in which the shock wave transomed into a stress wave, and could no longer break the rock.The duration of this stage was different, due to the different constraints of the slot and the shapes of the liners.However, it was generally longer than the first stage.The third stage was the residual wave stage, due to the interference of various reflected waves.The time-history curve of the strain continuously fluctuated due to the destruction of the rock mass by the detonation gas.Analysis of the strain variation revealed that this was in line with the stress conditions of the rock mass.The waveform fluctuations were primarily due to the differences in arrival time and magnitude of the peak strain at each measuring point.

| Peak strain analysis
The peak strains at each measuring point for the three samples are shown in Table 9 and Figure 12.
The peak strain at measuring point #2 in the combined energy-gathering direction was larger for the triangular liner than that for the arc-shaped and flat-top liners.At measuring points #8 and #9, the triangular liner produced the highest peak strain, while at measuring points #7 and #8, the order of the peak strain followed triangular liner > arc-shaped liner > flat-top liner.From the perspective of surrounding rock protection, the order of the three liners followed flat-top liner > arc-shaped liner > triangular liner, which was consistent with the actual model test results.Except for measuring point #2 for the arc-shaped liner, the peak strain values of measuring points #1-#3 in the combined energy-gathering direction were significantly greater than in the slot and nonenergy-gathering directions.Hence, the combined energy-gathering effect was better than the slot energy-gathering effect.For Sample No. 1, the peak strain at measuring point #1 was about twice that of measuring point #4.For Sample No. 2, the peak strain at measuring point #2 was about five and six times that of measuring points #5 and #8.For Sample No. 3, the peak strain at measuring point #2 was about five times that of measuring point #4 and about eight times that of measuring point #8.For measuring points #7-#9 in the nonenergy-gathering direction, the peak strain at measuring point #7 was the highest for the arcshaped liner, followed by the flat-top and triangular liners.At measuring point #8, the triangular liner had the highest peak strain, followed by the flat-top and arcshaped liners.At measuring point #9, the triangular liner had the highest peak strain, followed by the arc-shaped and flat-top liners.Under the same explosives and slot constraints, the triangular and arc-shaped liners had better results than the flat-top liner, from the perspectives of directional blasting and surrounding rock protection.Overall, the triangular liner demonstrated the best performance.

| CONCLUSIONS AND DISCUSSIONS
In this study, we investigated the influence of liner shape of combined charge liners, on the directional rockblasting effect of combined charges using theoretical analysis, numerical simulations, and model tests.The following conclusions were obtained.
(1) The formation of the energy-gathering jet, the pressure map, and the crack distribution were obtained using ANSYS/LS-DYNA software.We concluded that the arc-shaped liner and triangular liner outperformed the flat-top liner in terms of directional energy gathering.(2) Model tests were conducted using liners with three different shapes.Crack distribution was analyzed, and we found that the directional rock-blasting effect of the triangular liner was better than that of the arc-shaped liner and the flat-top liner.(3) The order of the peak strain in the combined energygathering direction followed triangular liner > arcshaped liner > flat-top liner, according to the peak strain at the same measuring point for different liners.The average peak strain in the combined energy-gathering direction was 2.3 times higher than in the nonenergy-gathering direction, and 2.1 times higher than in the single slot direction.The energygathering effect in the combined energy-gathering direction was significantly better than in the slot direction.The triangular and arc-shaped liners demonstrated a better directional blasting effect than the flat-top liner, with the triangular liner exhibiting the best overall performance.(4) According to the time-history waveform of strain, we found that the peak strain for the slotted tube on the liner side occurred earlier than in the single energygathering and nonenergy-gathering directions.Moreover, the peak strain in the combined energygathering direction initially increased and then decreased.The peak strain at measuring point #2 was the largest.(5) The results obtained from the model tests verified the numerical simulation findings.On the basis of the crack distribution and peak strain analysis, we concluded that under the same detonation conditions, the triangular liner exhibited the best performance in terms of directional blasting and directional damage risk reduction.
In conclusion, the triangular liner combined with polycap charge package has the best directional rockbreaking effect, which can be applied to directional controlled blasting, precracking blasting, and other engineering applications, but this test only carried out research on the shape of the polycap, and there are still deficiencies on the basis of the existing research, which still need to be improved in the future research.In the future, further research can be done on the material, angle, thickness, and other variables of the poly energy cover, and a multifactor coupling study can also be conducted on the above factors.

F
I G U R E 3 Schematic diagram of the cartridge.PVC, polyvinyl chloride.T A B L E 1 Relevant material parameters of the explosive.ρe (kg/m 3

4. 1 |
Equipment and test schemeGrade C30 concrete blocks (50 × 50 × 50 cm) were used in the model test, and the blast holes were 32 mm in diameter, with a depth of 30 cm.The samples used in this F I G U R E 4 Metal jets formed by different liners at T = 5.41 μs: (A) arc-shaped liner, (B) triangular liner, and (C) flat-top liner.F I G U R E 5 Pressure map of the different liners at T = 6.1 μs: (A) arc-shaped liner, (B) triangular liner, and (C) flat-top liner.F I G U R E 6 Crack distribution after the tests: (A) arc-shaped liner, (B) triangular liner, and (C) flat-top liner.

F I G U R E 7 8
Samples used in the model tests.T A B L E 7 Test parameters.Image of a combined-shaped charge.LIU ET AL.

F I G U R E 10
Cracks generated on the concrete samples in the model tests: (A) arc-shaped liner, (B) triangular liner, and (C) flat-top liner.F I G U R E 11 Strain waveforms of the (A) arc-shaped liner in the combined energy-gathering direction, (B) triangular liner in the combined energy-gathering direction, (C) flat-top liner in the combined energy-gathering direction, and (D) triangular liner in the nonenergy-gathering direction.

1 C 2 C 3 C 4 C 5 C 6
Relevant material parameters of the polyvinyl chloride tube.
T A B L E 3 | 4385 commercial concrete casting test blocks and packs.Where the packet is a combination of different poly energy cover poly energy packets, C30 strength commercial concrete casting test block is made of cement mortar poured in the mold.
T A B L E 9 Peak strain at each measuring point (με).
F I G U R E 12 Peak strains at the measuring points.